10-C-i

APPENDIX 10-C. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS

USING ALTERNATIVE PRODUCT PRICE FORECAST

TABLE OF CONTENTS

10-C.1 INTRODUCTION ............................................................................................... 10-C-1

10-C.2 DATA EVALUATION AND ANALYSIS......................................................... 10-C-1

10-C.3 NET PRESENT VALUE RESULTS USING ALTERNATIVE PRODUCT 

PRICE TREND.................................................................................................... 10-C-4

LIST OF TABLES

Table 10-C.3.1 NPV Using Alternative Product Price Forecast, Discounted at 3 

Percent, for Furnace Fans Used in HVAC Products Other than 

Hydronic Air Handlers (billion 2011$).................................................... 10-C-4

Table 10-C.3.2 Comparison of NPV Under Alternative Product Price Forecasts, 

Discounted at 3 Percent, for Furnace Fans Used in Non-Weatherized 

Gas Furnaces (billion 2011$)................................................................... 10-C-5

Table 10-C.3.3 NPV Using Alternative Product Price Forecast, Discounted at 7 

Percent, for Furnace Fans Used in HVAC Products Other than 

Hydronic Air Handlers (billion 2011$).................................................... 10-C-5

Table 10-C.3.4 Comparison of NPV Under Alternative Product Price Forecasts, 

Discounted at 7 Percent, for Furnace Fans Used in Non-Weatherized 

Gas Furnaces (billion 2011$)................................................................... 10-C-6

LIST OF FIGURES

Figure 10-C.2.1 Historical Normalized Prices of Warm Air Furnaces.............................. 10-C-2

Figure 10-C.2.2 Historical and Projected Total Shipments of Warm Air Furnaces .......... 10-C-2

Figure 10-C.2.3 Relative Price versus Cumulative Shipments of Warm Air Furnaces, 

with Power Law Fit.................................................................................. 10-C-3
10-C-1

APPENDIX 10-C. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS

USING ALTERNATIVE PRODUCT PRICE FORECAST

10-C.1 INTRODUCTION

The net present value (NPV) results presented in chapter 10 reflect a product price trend 

based on historic prices of electric motors. DOE also investigated the impact on the NPV for the 

considered CSLs for furnace fans of a product price forecast based on the experience curve 

approach. In DOE’s 2011 furnace standards rulemaking, it derived a forecast of furnace prices 

based on an analysis of the historic trend in the producer price index (PPI) for furnaces. In the

sensitivity analysis described in this appendix, DOE applied the experience curve developed for 

furnaces to the price of furnace fans.

The extensive literature on the “learning” or “experience” curve phenomenon is typically 

based on observations in the manufacturing sector.a In the experience curve method, the real cost 

of production is related to the cumulative production or “experience” with a manufactured 

product. This experience is usually measured in terms of cumulative production. A common 

functional relationship used to model the evolution of production costs in this case is:

Y = aX-b

where a is an initial price (or cost), b is a positive constant known as the experience rate 

parameter, X is cumulative production, and Y is the price as a function of cumulative production. 

Thus, as experience (production) accumulates, the cost of producing the next unit decreases. The 

percentage reduction in cost that occurs with each doubling of cumulative production is known 

as the experience rate (ER), given by:

ER = 1 – 2-b

In typical experience curve formulations, the experience rate parameter is derived using 

two historical data series: cumulative production and price (or cost). 

10-C.2 DATA EVALUATION AND ANALYSIS

To derive an experience rate for furnace fan products, DOE obtained historical Producer 

Price Index (PPI) data for furnaces from the Bureau of Labor Statistics’ (BLS). For warm air 

furnaces, DOE used PPI data spanning the period 1990-2010. An inflation-adjusted price index

for warm air furnaces was calculated by dividing the PPI series by the Consumer Price Index 

(CPI) “all items” index for the same years. This inflation-adjusted price index (shown in Figure 

10-C.2.1) was used in subsequent analysis steps.

 

a Weiss, M., Junginger, H.M., Patel, M.K., Blok, K., (2010a). A Review of Experience Curve Analyses for Energy 

Demand Technologies. Technological Forecasting & Social Change. 77:411-428. 
10-C-2

Figure 10-C.2.1 Historical Normalized Prices of Warm Air Furnaces

DOE assembled a time-series of annual shipments for 1953-2009 for furnaces using data from 

AHRI and the Gas Appliance Manufacturers Association. For furnaces, shipments prior to 1953 

were extrapolated backward based on a linear trend to the historical shipments. The annual 

shipments data were used to estimate cumulative shipments (production). Projected shipments 

after 2009 were obtained from the base case projections made for the NIA (see chapter 9 of this 

TSD). Figure 10-C.2.2 shows the shipments time series used in the analysis.

Figure 10-C.2.2 Historical and Projected Total Shipments of Warm 

Air Furnaces

To estimate an experience rate parameter, a least-squares power-law fit was performed on 

the unified price index versus cumulative shipments (See Figure 10-C.2.3).

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

1920 1940 1960 1980 2000 2020 2040 2060

Annual Total Shipments (millions)

Year

Historical

Projected

Extrapolated
10-C-3

Figure 10-C.2.3 Relative Price versus Cumulative Shipments of 

Warm Air Furnaces, with Power Law Fit

The form of the fitting equation is:

P(X) = PoX-b

,

where the two parameters, b (the experience rate parameter) and Po (the price or cost of the first 

unit of production), are obtained by fitting the model to the data. DOE notes that the cumulative 

shipments on the right hand side of the equation can have a dependence on price, so there is an 

issue with simultaneity where the independent variable is not truly independent. DOE’s use of a 

simple least squares fit is equivalent to an assumption of no significant first price elasticity 

effects in the cumulative shipments variable.

The parameter values obtained are:

Po = 13.18−3.02

+3.92 (95% confidence), and 

b = 0.527±0.056 (95% confidence).

For warm air furnaces, the estimated experience rate (defined as the fractional reduction 

in price expected from each doubling of cumulative production) is 30.6−2.7

+2.6% (95% confidence). 

DOE then derived a price factor index, with 2010 equal to 1, to forecast prices in each 

future year in the analysis period. The index value in a given year is a function of the LR and the 

cumulative production forecast through that year. DOE applied the same value to forecast prices 

for each furnace fan product class at each considered efficiency level.

y = 13.184x-0.527

R2 = 0.954

0.8

0.9

1.0

1.1

1.2

1.3

1.4

60 80 100 120 140 160

Relative Price (2010=1)

Cumulative Shipments (millions)

Historical

Learning Fit
10-C-4

10-C.3 NET PRESENT VALUE RESULTS USING ALTERNATIVE 

PRODUCT PRICE TREND

This section presents the NPV results using the alternative product price forecast for each 

key product class. For non-weatherized gas furnace fans, it also compares the NPV using the 

default product price forecast with the NPV using the alternative product price forecast.

Table 10-C.3.1 NPV Using Alternative Product Price Forecast, Discounted at 3 Percent, 

for Furnace Fans Used in HVAC Products Other than Hydronic Air 

Handlers (billion 2011$)

Key Product Class Candidate Standard Level

1 2 3 4 5

Improved 

PSC

PSC w/ 

Controls

X13 ECM ECM + 

Backward

-curved 

Impeller

Non-weatherized, Non-condensing 

Gas Furnace Fan 0.113 0.077 4.536 0.865 1.776

Non-weatherized, Condensing Gas 

Furnace Fan 0.257 1.584 4.516 0.498 1.481

Weatherized Gas Furnace Fan 0.007 0.087 0.854 0.439 0.657

Oil Furnace Fan 0.024 0.206 0.145 -0.016 -0.032

Electric Furnace / Modular Blower 

Fan 0.010 -0.110 0.610 -0.461 -0.276

Manufactured Home Nonweatherized, Non-condensing Gas 

Furnace Fan

0.003 0.024 0.049 -0.044 -0.048

Manufactured Home Nonweatherized, Condensing Gas Furnace 

Fan

0.005 0.036 0.049 -0.084 -0.101

Manufactured Home Electric Furnace 

/ Modular Blower Fan -0.001 0.011 0.042 -0.075 -0.027
10-C-5

Table 10-C.3.2 Comparison of NPV Under Alternative Product Price Forecasts, 

Discounted at 3 Percent, for Furnace Fans Used in Non-Weatherized Gas 

Furnaces (billion 2011$)

Candidate Standard Level

1 2 3 4 5

Improved 

PSC

PSC w/ 

Controls

X13 ECM ECM + 

Backward

-curved 

Impeller

Non-weatherized, Non-condensing Gas Furnace Fan

 Default Price Trend 0.110 0.048 4.462 0.551 1.395

 Price Trend Based on Experience

 Curve for Furnaces 0.113 0.077 4.536 0.865 1.776

Non-weatherized, Condensing Gas Furnace Fan

 Default Price Trend 0.254 1.559 4.449 0.089 0.944

 Price Trend Based on Experience

 Curve for Furnaces 0.257 1.584 4.516 0.498 1.481

Table 10-C.3.3 NPV Using Alternative Product Price Forecast, Discounted at 7 Percent, 

for Furnace Fans Used in HVAC Products Other than Hydronic Air 

Handlers (billion 2011$)

Key Product Class Candidate Standard Level

1 2 3 4 5

Improved 

PSC

PSC w/ 

Controls

X13 ECM ECM + 

Backward

-curved 

Impeller

Non-weatherized, Non-condensing Gas 

Furnace Fan 0.037 -0.021 1.587 -0.138 0.091

Non-weatherized, Condensing Gas 

Furnace Fan 0.096 0.575 1.650 -0.323 -0.155

Weatherized Gas Furnace Fan 0.002 0.030 0.346 0.107 0.166

Oil Furnace Fan 0.008 0.071 0.040 -0.039 -0.052

Electric Furnace / Modular Blower Fan 0.003 -0.055 0.233 -0.301 -0.272

Manufactured Home Non-weatherized, 

Non-condensing Gas Furnace Fan 0.001 0.005 0.013 -0.041 -0.046

Manufactured Home Non-weatherized, 

Condensing Gas Furnace Fan 0.002 0.013 0.017 -0.058 -0.070

Manufactured Home Electric Furnace / 

Modular Blower Fan -0.001 0.000 0.011 -0.064 -0.046
10-C-6

Table 10-C.3.4 Comparison of NPV Under Alternative Product Price Forecasts, 

Discounted at 7 Percent, for Furnace Fans Used in Non-Weatherized Gas 

Furnaces (billion 2011$)

Candidate Standard Level

1 2 3 4 5

Improved 

PSC

PSC w/ 

Controls

X13 ECM ECM + 

Backward

-curved 

Impeller

Non-weatherized, Non-condensing Gas Furnace Fan

 Default Price Trend 0.037 -0.021 1.587 -0.138 0.091

 Price Trend Based on Experience

 Curve for Furnaces 0.037 -0.029 1.566 0.206 0.412

Non-weatherized, Condensing Gas Furnace Fan

 Default Price Trend 0.095 0.564 1.618 -0.505 -0.392

 Price Trend Based on Experience

 Curve for Furnaces 0.096 0.575 1.650 -0.323 -0.155